Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.
$3 x^{2} + 11 x + 10 = 0$

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Solution

The given equation is
Now,
$x squared plus 11 over 3 x plus 10 over 3 equals 0 rightwards double arrow x squared plus 2 cross times 11 over 6 x plus left parenthesis 11 over 6 right parenthesis squared minus left parenthesis 11 over 6 right parenthesis squared plus 10 over 3 equals 0 rightwards double arrow left parenthesis x plus 11 over 6 right parenthesis squared equals left parenthesis 11 over 6 right parenthesis squared minus 10 over 3 equals 121 over 36 minus 10 over 3 rightwards double arrow left parenthesis x plus 11 over 6 right parenthesis squared equals fraction numerator 121 minus 10 cross times 12 over denominator 36 end fraction equals 1 over 36 rightwards double arrow x plus 11 over 6 equals plus-or-minus 1 over 6 rightwards double arrow x equals negative 11 over 6 plus-or-minus 1 over 6 rightwards double arrow x equals negative 12 over 6 space o r space minus 10 over 6 rightwards double arrow space x equals negative 2 space o r space minus 5 over 3$

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